where \(\rho \)  represents thread density, which is defined as the sum of the lengths of threads per unit volume or the maximal number of threads across a unit disk [1]}. Actually the two definitions are technically subtly different, see the discussion in [1]}., i.e.,
\(\rho \left( {{{\vec{v}}_{t\tilde{T}}}} \right) = \left| {{{\vec{v}}_{t\tilde{T}}}} \right|.\) 
